Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3

Figure 2 – Single Segment Strap Assembly Version 3 with G10/ 304 SS Supports G10 Support 304 SS Support

Figure 3 – Single Segment Strap Assembly: Center Strap Only

B tor = 1 T I = 130 kA B pol =.3 T U rad thermal =.018 in U vert thermal =.3 in 38 Laminations: -.060” thk;.005” gap Mat’l: Copper Wt full = 37.4 lb (Wt arch = 20.4 lb) 2” 2.523” 7.5” R in = 3.160” R out = 5.688” 5” Figure 4 – Single Laminated Strap Assembly with Applied Fields and Current

x x x x x x x x x x x x x x x x x x Out-of-Plane Load (z-direction) F op = 2*I*B pol *R F op = 2 x 130,000 A/ 38 x.3 T x 5.688/39.37 m F op = N = 66.6 lbf [per lamination] In-Plane Load (y-direction) F ip / L = I*B tor F ip / L = 130,000 A/ 38 x 1 T [per lamination] F ip / L = 3,421 N/ m x.2248 lbf/ N x 1 m/ in F ip / L = lbf/ in press ip = (F ip / L)/ w press ip = lbf/in / 2 in press ip = 9.77 lbf/ in 2 (applied to inside cylindrical faces) Calculated EMAG Loads B pol B tor I+I+ I+I+ R w F op press ip

Figure 5A – Single Lamination FEA Model: Mesh and Boundary Conditions 3 Elements thru Thickness Ux =.018 in Uy =.3 in Uz = 0 Press = 9.7 psi Force = 66.6 lbf Fixed

Figure 5B – Single Lamination Linear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Figure 5C – Single Lamination Linear Results: von Mises Stress Loads: Thermal Displacements Only

Figure 5D – Single Lamination Linear Results: von Mises Stress Loads: In-Plane (Pressure) Load Only

Figure 5E – Single Lamination Linear Results: von Mises Stress Loads: Out-of-Plane (Force) Load Only

Large deflection = On Figure 5F – Single Lamination Nonlinear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Baseline-Design MathCAD Flex Strap Lamination Analysis: Conclusions/ Recommendations ~3/4 overall stiffness due to Inner Strap Assy OOP torsional stress dominates in Outer Strap Assy; thermal displacement bending dominates in Inner Strap Assy OOP force proportional to radius Thermal displacement bending stress inversely proportional to radius Deflection force inversely proportional to radius Proposed Design: –Outer Assy: 12X.090” thick, 2.2” wide laminations –Inner Assy: 19X.060” thick, 2.0” wide laminations –Mat’l: Fully-hardened OFHC or Cu-Zr

Baseline Design Proposed Design ASM International, “Atlas of Stress-Strain Curves”, Electrolytic Tough-Pitch Copper (C11000) Figure 5G – Copper Stress-Strain Curves versus % Cold Work Baseline Design and Proposed Design Combined-Load Stresses Shown

Baseline Design Proposed Design NIST Monograph 177, “Properties of Copper and Copper Alloys at Cryogenic Temperatures” Figure 5H – Copper Fatigue S-N Curves versus % Cold Work Baseline Design and Proposed Design Combined-Load Stresses Shown

Figure 5J – Single Lamination Nonlinear Results: Z-Deformations Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP) Large deflection = On

Figure 5K – Single Lamination Nonlinear Results: Z-Deformations_Front Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP) Large deflection = On

Figure 5L – Single Lamination Nonlinear Results: von Mises Stress Loads: Emag Pressure (In Plane) Only Large deflection = On σ hoop = P*R/ t = 9.77 psi x in/.060 in = 924 psi

Figure 5M – Single Lamination Pre-Stressed Linear Buckling Results Load multiplier LMF applies to all Emag loads and thermal displacements 1 st Mode Load Multiplier = nd Mode Load Multiplier = rd Mode Load Multiplier = Large deflection = Off 1 st Mode Load Multiplier = 58.4 (Nonlinear 1 st Mode Load Multiplier = 50)

Figure 5N – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (1) Load multiplier factor LMF applies only Out-of-Plane Emag load Large deflection = On Y 080 LMF = 14

Figure 5P – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (2) Load multiplier factor LMF applies only to Out-of-Plane Emag load Large deflection = On LMF = 26 Y 080

Conclusions Buckling due mostly to out-of-plane load. In- plane load (pressure outward) reduces buckling; thermal displacements slightly increase buckling. Good agreement between linear and nonlinear buckling results with load multiplier factor applied to both Emag loads and to thermal displacements. Load multiplier factor over 14 for nonlinear analysis with constant in-plane load and increasing out-of-plane load (conservative).

Figure 6A – 3 Lamination FEA Model: Mesh 3 Elements / Lamination

Large deflection = On Frictional contact (COF =.4) Figure 6B – 3 Lamination Nonlinear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Figure 6C – 3 Lamination Nonlinear Results: Z-Deformations Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP) Large deflection = On Frictional contact (COF =.4)

Figure 6D – 3 Lamination Nonlinear Results: Z-Deformations_Front Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP) Large deflection = On Frictional contact (COF =.4)

Figure 6E – 3 Lamination Nonlinear Results: Contact Status Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP) Large deflection = On Frictional contact (COF =.4)

Figure 6F – 3 Lamination Results: Linear Buckling Mode Multiplier Load Multiplier factor LMF applies to all Emag loads and thermal displacements Large deflection = Off Frictional contact (COF =.4) 1 st Mode Load Multiplier = nd Mode Load Multiplier = rd Mode Load Multiplier = 61.8

Figure 7A – Single Laminated Strap Assembly FEA Model: Bonded and Frictionless Contact Areas

3 elements/ lamination Figure 7B – Single Laminated Strap Assembly FEA Model: Mesh # Nodes = # Elements =

Fig. 7C –Laminated Strap Assembly FEA Results - Thermal Displacements Only: von Mises Stress Large deflection = Off Frictional contact (COF = 0)

Fig. 7D –Laminated Strap Assembly FEA Results – Thermal Displacements Only: Total Deformation Large deflection = Off Frictional contact (COF = 0)

T nodes Heat Gen JS F Lorentz B y =.3T B z = 1 T I = 130 kA Non-Linear Large Deflection Non-Linear Large Deflection Fig. 8A – Upper Flex Strap ANSYS Multiphysics Analysis Work Flow Diagram u x =.018” u y =.30”

Figure 8B – Single Segment_Center Strap Assembly: Mesh

Fig. 9C – Single Segment_Center Strap Electric Model: Boundary Conditions 130,000 A 0 V

Figure 8D – Single Segment_Center Strap Electric Model Results: Voltage

Fig. 8E – Single Segment_Center Strap Electric Model Results: Current Density

Fig. 8F – Single Segment_Center Strap Electric Model Results: Joule Heat